A248023 Even numbers which are neither primes nor perfect powers and are coprime to the sum of their divisors.

50, 98, 242, 338, 392, 578, 722, 800, 968, 1058, 1250, 1352, 1682, 1922, 2312, 2450, 2738, 2888, 3362, 3698, 3872, 4232, 4418, 4802, 5408, 5618, 6050, 6272, 6728, 6962, 7442, 7688, 8450, 8978, 9248, 10082, 10658, 10952, 11552, 12482, 12800, 13448, 13778, 14450

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1500

Example

50 is in the sequence since it is neither a prime nor a powerful number and its divisors 1, 2, 5, 10, 25, and 50 sum to 93, which is coprime to 50.

Mathematica

perfectPowerQ[n_] := n == 1 || GCD @@ FactorInteger[n][[All, 2]] > 1; Select[ 2 Range@ 7500, !PrimeQ[ #] && GCD[#, DivisorSigma[1, #]] == 1 && !perfectPowerQ[ #] &]

Prog

(PARI) lista(nn) = {forstep(n=4, nn, 2, if (!ispower(n) && (gcd(n, sigma(n))==1), print1(n, ", ")); ); } \\ Michel Marcus, Oct 02 2014

Crossrefs

Cf. A003624, A106543, A248020.

Sequence in context: A260901 A090997 A141757 * A328253 A044139 A044520

Adjacent sequences: A248020 A248021 A248022 * A248024 A248025 A248026

Keyword

nonn,easy

Author

Robert G. Wilson v, Sep 29 2014

Status

approved